Summary: One of the most unique characteristics of man is his ability to imagine and contemplate things that are abstract, and one of the most difficult of all abstract ideas is the concept of numbers. But man is not the only one who uses numbers to perform mathematical computations. This article looks at how nature itself uses math.
One of the most unique characteristics of man is his ability to imagine and contemplate things that are abstract, which are things we can’t see or experience with our senses, and one of the most difficult of all abstract ideas is the concept of numbers. But over time man has learned to take this concept to a higher level as he’s learned to manipulate those numbers in what we call mathematics.
Starting with the simple concept of adding and subtracting, man learned the shortcuts of multiplication and division. Then came the more difficult concept of equating one set of numbers to another set, which led to the development of algebra, geometry, trigonometry, and calculus. And along the way man also developed the concept of statistical analysis and created formulas that help him to understand the laws of probability. Today, there are twenty-six different variations of mathematics.
All of the higher forms of math deal with unknown numbers, such as x+2=4. In this problem, we don’t know what the numerical value is for x and the way we discover what that number should be is called algebra. But then man began to create equations where there can be multiple unknown numbers, such as z+y=x. In cases like this, such equations can have multiple correct answers depending on what numbers are for x and y. All these concepts are far beyond the ability of all living organisms to comprehend except that of man.
However, as scientists have explored our environment, including such sciences as geology, biology, meteorology, astronomy, as well as many others, they’ve discovered they were able to convert the laws of nature into mathematical formulas, and as they did, what they further discovered is that all of nature seems to have built within it a complex mathematical blueprint that it follows.
For example, from our natural perspective, weather appears to be random and unpredictable in how it occurs, but as scientists have explored our environment, including such sciences as geology, biology, meteorology, astronomy, as well as many others, they’ve discovered they were able to convert the laws of nature into mathematical formulas, and as they did, what they further discovered is that all of nature seems to have built within it a complex mathematical blueprint that it follows.
What science knows is that inside the cell of every living organism is something called DNA which contains a blueprint that the cell uses to know how to function, to build, repair, and duplicate itself. We know that the information is based on a very simple concept of numbers, but what science has also discovered is that embedded in each DNA is an array of very complex mathematical formulas that determines what the overall structure of the living organism will look like and how it will behave.
To illustrate this, when we purchase a computer, it comes with various kinds of programs that have mathematical formulas already built into it and it’s when the user puts certain information into the computer, that the program then is able to calculate what the user wants it to do.
Take for example, when using a digital spreadsheet, the user provides numbers they want added and based on those numbers the built-in program automatically adds them together (y+z) and gives them the answer they’re looking for. (x). Of course, when a different set of numbers is used, the same equation will then produce a different answer.
Although this is a very simple equation, computer programmers can put in whatever kind of equation they want, no matter how complicated it may be. For example, the formula could be 6(3x-2y)(x-2)/4., and once it’s put into the computer, whenever the user puts in the valve for y and x, the computer will always give them the answer they’re looking for, and they can do this over and over again using different numbers for y and x
This is what meteorologists do because the computer they use to predict the weather already has built into it a series of very complex equations, and all the meteorologists have to do is put in the necessary information and the built in formulas automatically calculate what the weather will be like in the future.
In the same way, if there is a mathematical equation already programmed into the DNA of every plant and animal, then whatever variations already exist in the DNA of that particular organism, will be used by the pre-programed formula to determine what the end result will be. Since there are many different variables that can be put into that mathematical formula then there can be a wide variety of different outcomes.
For example, this is what accounts for parents who have blue eyes who can have a child with green eyes, and there is a formula, known as Punnet Square that can predict the probability of these differences based on the information contained in the DNA.
One of the more intricate things that has been discovered in nature is something called fractals. These are made from a pattern that keeps repeating itself at different scales.
This was discovered by a mathematician named Benoit Mandalbrot, and his formula for how fractals work is f(Z) = Z2 + C, which simply means that you take a number (Z), square it, add it to the original number (C), and then repeatt the process all over again. But this formula works equally as well with patterns, and as we look at nature, what appears to be something chaotic, is actually a complex series of repeating patterns that follows Mandalbrot’s formula.
We see this all throughout nature. We see it in the shape of snowflakes, in spider webs, tree structure, and in the veins of leaves. We see it in the structure of lungs, blood vessels, nerves, kidneys, brain cells and other organs in the body.
But more than this, we’ve come to see that the entire universe is inherently mathematical as Einstein discovered when he developed his famous formula, E=MC2, which explains how energy is derived from the mass of an object. For this reason, mathematics is the basis for studying all the many and various laws of physics. For example, we see it in the way weather behaves, in the trajectory of asteroids, how atoms interact with one another, and even how galaxies are formed.
The question scientists have debated is whether all the math we see in nature is just an invention of man, or whether man has merely discovered the math that already exists in nature? Stated differently, is it man’s inventive mind that has created a way to turn anything into a mathematical formula, or does nature truly operate according to the rules of mathematics?
All of nature can be seen as patterns, and all patterns can be stated in mathematical terms. For example, a square is a pattern that links four lines together where two opposite sides are equal to one another, and the other two lines are equal to one another. A triangle is made of three lines linked together and are made by using three angles that alway add up to 180 degrees. A circle is made from one line connected to itself where all parts of the line are the same distance from the center of the circle, and all of these shapes can be described mathematically.
Atoms have a center made of neutrons and protons, with one or more electrons orbiting them. We can measure the electrical charge of the electron, and we can also determine how many protons and how many neutrons are in the center of an atom by how many electrons a particular atom has. In addition to this, we can measure the weight of each kind of atom.
Light is made of photons that travel through space in the form of a wave pattern, and there are different kinds of waves. Depending on the distance between them will determine whether it is a radio wave, a microwave, an infrared wave, a visible light wave, an ultraviolet wave, an x ray wave or a gamma ray wave.
Sound likewise travels in wave patterns and because of this, we can measure the distance between waves as well as the distance between the crest and troughs of a wave. We can also measure the speed of a wave. Therefore, anything that can be measured is something that can be expressed using mathematics.
Allen Turning was a brilliant mathematician who was able to mathematically decipher the German’s famous WWII Enigma code that was thought to be impossible to crack. In 1952 he published an article called “The Chemical Basis of Morphogenesis” in which he proposed that the diversity we see in nature can all be explained mathematically.
The very nature of mathematics is based on its ability to be totally consistent. For example, 1 plus 1 is always 2 under any and all circumstances as is 2 times 2 equals 4. If a mathematical formula is not consistent under all similar conditions, then such a formula has to be wrong.
Nature is extremely complex and there are many different factors to consider when trying to uncover its secrets, but as scientists have taken Turning’s formula and applied it to many different forms of living organisms, from cell division, to the spiral arrangement of petals on a flower, or the tentacles of a hydra, or the spots on a leopard or the stripes on a zebra, and even the waves on a sand dune, they’ve found that his formula has proven to be very effective in explaining all these many and varied patterns
Although there are some who want to say that all these mathematical formulas used to explain nature are nothing more than inventions of man, yet the vast majority of scientists and some of the greatest minds in mathematics are convinced that nature operates according to the rules of mathematics and that man is merely discovering what those rules are.
When we talk about the laws of nature, the word law, by its very definition, is something that cannot change. For example, the law of gravity works the same everywhere throughout the universe. Light always travels at 186,000 miles per second. That never changes. And because natural law is constant, then it can be expressed in terms of a mathematical formula.
In 2024 Michel Talagrand received the equivalent of the Nobel prize in mathematics for his theory of probability of randomness. What that means is, that through the use of the mathematical formulas he developed, he has shown that what seems to be random occurrences throughout all of nature can be predicted with precise estimates. For example, he’s been able to predict the movement of gas molecules and how to anticipate the growth of bacteria. This is something no one had previously thought possible, and as a result, his work has proven to have important application in the fields of physics, chemistry, communications, and ecology.
What this tells us is that nature does not operate on the basis of random, arbitrary, and unpredictable changes, In other words, what looks like chaos, turmoil, and disarray to the untrained and unsophisticated eye, actually has order and purpose to it.
The great German philosopher, Immanuel Kant understood this when he said, “Nature, even in chaos, cannot proceed otherwise than regularly and according to order. Nature, when left to universal law, tends to produce regularity out of chaos.”
If that is true, then this is clear evidence that what we see in nature operates according to complex mathematical laws. If we were to see this happen in just one isolated case in nature, we might argue that such a thing could possibly have happened by accident, but when we see mathematical precision all throughout nature, the only explanation is that someone who is extremely intelligent deliberately designed all of nature to operate the way it does.
Man didn’t invent math; he discovered something that has existed from the beginning, which is why math is natural.
Related articles can be found at Foundation of Fatih – Parting thoughts, and Parting Thoughts